As the players walked off the pitch following Saturday's third ODI, footage showed Shehzad telling Dilshan: "If you are a non-Muslim and you turn Muslim, no matter whatever you do in your life, straight to heaven."
Following Dilshan's reply, which was inaudible, Shehzad was further heard saying: "Then be ready for the fire."
PCB Chairman Shaharyar Khan said Shehzad had violated clauses of his central contract.
"There is a clause which states clearly players should not indulge in talk of religious or political nature in public while representing Pakistan," Khan told reporters on Friday.
"Shehzad has violated this clause on evidence of what we have seen in the video footage of the incident."
Shehzad, who has played five tests and 48 ODIs, has had disciplinary problems since making his debut for the national under-19 team.
He was reported as a junior player for curfew violations and has had counselling sessions organised by the board. Khan said the Sri Lankan board had not complained about the incident.
Shehzad, 22, has said it was just banter with Dilshan and he meant nothing by it.
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O' Lord Almighty please save Islam from Muslims (Amen)
I apologize on behalf of my brother, that was out of character of him -he's young so I hope everybody can excuse this gaffe of his.